Define the following parameters for a switching network:

$N=$ number of hops between two given end systems

$L=$ message length in bits

$B=$ data rate, in bits per second $($bps$),$ on all links

$P=$ fixed packet size, in bits

$H=$ overhead $($header$)$ bits per packet

$S=$ call setup time $($circuit switching or virtual circuit$)$ in seconds

$D=$ propagation delay per hop in seconds

For $N=4,L=3200,B=9600,P=1024,H=16,S=0\mathrm{.}2,D=0\mathrm{.}001,$ compute the end$-$to$-$end delay for circuit switching, virtual circuit packet switching, and datagram packet switching. Assume that there are no acknowledgments. Ignore processing delay at the nodes.

Derive general expressions for the three techniques of part $($a$),$ taken two at a time $($three expressions in all$),$ showing the conditions under which, the delays are equal.